Jesse Ventura was governor of Minnesota, and Arnold Shwarzenegger is the current governor of California. The fight takes place in the film "the Running Man", which was released in 1987 and based on a novel by Stephen King, writing as Richard Bachman, which had a very different ending.
Richards overpowers the flight crew but is shot, suffering a mortal wound. With his last strength, he overrides the plane's autopilot and sets the plane to fly right into the Games Building, home of the Network and "The Running Man". The last thing Killian sees is Richards in the cockpit giving him the finger as the plane slams into the building.
King wrote this as Bachman, and Bachman is not real. The fight scene in the film is a fiction within a fiction, computer generated images intended to trick the audience into thinking Richards (Schwarzenegger) is dead.
This is the cover of the novel, which reads....
Welcome to America in 2025, where the best men don't run for president, they run for their lives.
Schwarzenegger and Ventura were both "running men", in the film and in politics. There has been speculation that both men may someday run for president. If that happens, I'm voting for Jesse.